{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DYORX34FTIZ5VV5DOVDMQZKNQD","short_pith_number":"pith:DYORX34F","schema_version":"1.0","canonical_sha256":"1e1d1bef859a33dad7a37546c8654d80d026450ed498b4a7d98cda2b7813ad60","source":{"kind":"arxiv","id":"1506.02731","version":2},"attestation_state":"computed","paper":{"title":"Entire solutions of quasilinear symmetric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Mostafa Fazly","submitted_at":"2015-06-08T23:49:17Z","abstract_excerpt":"We study the following quasilinear elliptic system for all $i=1,\\cdots,m$ \\begin{equation*} \\label{}\n  -div(\\Phi'(|\\nabla u_i|^2) \\nabla u_i) = H_i(u) \\quad \\text{in} \\ \\ \\mathbb{R}^n\n  \\end{equation*} where $u=(u_i)_{i=1}^m: \\mathbb R^n\\to \\mathbb R^m$ and the nonlinearity $ H_i(u) \\in C^1(\\mathbb R^m)\\to \\mathbb R$ is a general nonlinearity. Several celebrated operators such as the prescribed mean curvature, the Laplacian and the $p$-Laplacian operators fit in the above form, for appropriate $\\Phi$. We establish a Hamiltonian identity of the following form for all $x_n\\in\\mathbb R$ \\begin{eq"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.02731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-08T23:49:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"596b296ae4f885bc39356e285eb5e23fd1598a4d41e438ca24b4d44151850087","abstract_canon_sha256":"c4b87f7f4ca84d6652f2e7591ee3beaea0e2f5185ae2cafabab97ad69d81320f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:14.116382Z","signature_b64":"kaloK7LJpnKLsCySGtWyae55+s1Ucw+WvYAkNX3+cqHFYPT3/L+IwfO1souDXn0lYg/bCPnoCCRS677IfyErAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e1d1bef859a33dad7a37546c8654d80d026450ed498b4a7d98cda2b7813ad60","last_reissued_at":"2026-05-18T01:28:14.115611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:14.115611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entire solutions of quasilinear symmetric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Mostafa Fazly","submitted_at":"2015-06-08T23:49:17Z","abstract_excerpt":"We study the following quasilinear elliptic system for all $i=1,\\cdots,m$ \\begin{equation*} \\label{}\n  -div(\\Phi'(|\\nabla u_i|^2) \\nabla u_i) = H_i(u) \\quad \\text{in} \\ \\ \\mathbb{R}^n\n  \\end{equation*} where $u=(u_i)_{i=1}^m: \\mathbb R^n\\to \\mathbb R^m$ and the nonlinearity $ H_i(u) \\in C^1(\\mathbb R^m)\\to \\mathbb R$ is a general nonlinearity. Several celebrated operators such as the prescribed mean curvature, the Laplacian and the $p$-Laplacian operators fit in the above form, for appropriate $\\Phi$. We establish a Hamiltonian identity of the following form for all $x_n\\in\\mathbb R$ \\begin{eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02731","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.02731","created_at":"2026-05-18T01:28:14.115724+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.02731v2","created_at":"2026-05-18T01:28:14.115724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02731","created_at":"2026-05-18T01:28:14.115724+00:00"},{"alias_kind":"pith_short_12","alias_value":"DYORX34FTIZ5","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DYORX34FTIZ5VV5D","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DYORX34F","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD","json":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD.json","graph_json":"https://pith.science/api/pith-number/DYORX34FTIZ5VV5DOVDMQZKNQD/graph.json","events_json":"https://pith.science/api/pith-number/DYORX34FTIZ5VV5DOVDMQZKNQD/events.json","paper":"https://pith.science/paper/DYORX34F"},"agent_actions":{"view_html":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD","download_json":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD.json","view_paper":"https://pith.science/paper/DYORX34F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.02731&json=true","fetch_graph":"https://pith.science/api/pith-number/DYORX34FTIZ5VV5DOVDMQZKNQD/graph.json","fetch_events":"https://pith.science/api/pith-number/DYORX34FTIZ5VV5DOVDMQZKNQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD/action/storage_attestation","attest_author":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD/action/author_attestation","sign_citation":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD/action/citation_signature","submit_replication":"https://pith.science/pith/DYORX34FTIZ5VV5DOVDMQZKNQD/action/replication_record"}},"created_at":"2026-05-18T01:28:14.115724+00:00","updated_at":"2026-05-18T01:28:14.115724+00:00"}